Semi infinite body, steady 1-D.

X10 Semi-infinite body, 0 < x < $\infty$, with G = 0 (Dirichlet) at x = 0.

$$\left\vert\vphantom{ \,x^{\prime }}\right. \prime \left.\vphantom{ \,x^{\prime }}\right. \left\{\vphantom{ \begin{array}{cc} x & \text{for }x<x^{\prime } \\ x^{\prime } & \text{for }x>x^{\prime } \end{array} }\right. \begin{array}{cc} x & \text{for }x<x^{\prime } \\ x^{\prime } & \text{for }x>x^{\prime } \end{array} \left.\vphantom{ \begin{array}{cc} x & \text{for }x<x^{\prime } \\ x^{\prime } & \text{for }x>x^{\prime } \end{array} }\right.$$

X20 Semi-infinite body, 0 < x < $\infty$, with $\partial$G/$\partial$x = 0 (Neumann) at x = 0. Note that this geometry requires a pseudo GF, denoted H. The temperature solution found from a pseudo GF requires that the total volumetric heating sums to zero and the spatial average temperature in the body must be supplied as a known condition.

$$\left\vert\vphantom{ \,x^{\prime }}\right. \prime \left.\vphantom{ \,x^{\prime }}\right. \left\{\vphantom{ \begin{array}{cc} -x^{\prime } & \text{for }x<x^{\prime } \\ -x & \text{for }x>x^{\prime } \end{array} }\right. \begin{array}{cc} -x^{\prime } & \text{for }x<x^{\prime } \\ -x & \text{for }x>x^{\prime } \end{array} \left.\vphantom{ \begin{array}{cc} -x^{\prime } & \text{for }x<x^{\prime } \\ -x & \text{for }x>x^{\prime } \end{array} }\right.$$

X30 Semi-infinite body, 0 < x < $\infty$, with - k$\partial$G/$\partial$x + hG = 0 (convection) at x = 0.

$$\left\vert\vphantom{ \,x^{\prime }}\right. \prime \left.\vphantom{ \,x^{\prime }}\right. \left\{\vphantom{ \begin{array}{cc} -\left( \frac{hx}{k}+1\right... ...rac{hx^{\prime }}{k}+1\right) x & \text{for }x>x^{\prime } \end{array} }\right. \begin{array}{cc} -\left( \frac{hx}{k}+1\right) x^{\prime } & \te... ...\left( \frac{hx^{\prime }}{k}+1\right) x & \text{for }x>x^{\prime } \end{array} \left.\vphantom{ \begin{array}{cc} -\left( \frac{hx}{k}+1\right)... ...rac{hx^{\prime }}{k}+1\right) x & \text{for }x>x^{\prime } \end{array} }\right.$$